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arXiv · 1308.0724

On the decay of elements of inverse triangular Toeplitz matrix

Neville Ford·D. V. Savostyanov·N. L. Zamarashkin
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Abstract

We consider half-infinite triangular Toeplitz matrices with slow decay of the elements and prove under a monotonicity condition that elements of the inverse matrix, as well as elements of the fundamental matrix, decay to zero. We also provide a quantitative description of the decay of the fundamental matrix in terms of p-norms. Finally, we prove that for matrices with slow log-convex decay the inverse matrix has fast decay, i.e. is bounded. The results are compared with the classical results of Jaffard and Veccio and illustrated by numerical example.

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Neville Ford, D. V. Savostyanov, N. L. Zamarashkin. 2013-08-03. On the decay of elements of inverse triangular Toeplitz matrix. https://doi.org/10.1137/130931734

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